Question: Simplify; express your answer in exponential form. Assume $k\neq 0, p\neq 0$. $\dfrac{{(k)^{-3}}}{{(k^{2}p^{3})^{4}}}$
To start, try working on the numerator and the denominator independently. In the numerator, we have ${k}$ to the exponent ${-3}$ . Now ${1 \times -3 = -3}$ , so ${(k)^{-3} = k^{-3}}$ In the denominator, we can use the distributive property of exponents. ${(k^{2}p^{3})^{4} = (k^{2})^{4}(p^{3})^{4}}$ Simplify using the same method from the numerator and put the entire equation together. $\dfrac{{(k)^{-3}}}{{(k^{2}p^{3})^{4}}} = \dfrac{{k^{-3}}}{{k^{8}p^{12}}}$ Break up the equation by variable and simplify. $\dfrac{{k^{-3}}}{{k^{8}p^{12}}} = \dfrac{{k^{-3}}}{{k^{8}}} \cdot \dfrac{{1}}{{p^{12}}} = k^{{-3} - {8}} \cdot p^{- {12}} = k^{-11}p^{-12}$.